Yes, I have heard of it. Borean effectively is a superset of Altaic or the even more controversial Nostratic. The languages of Iberia 3000 years ago, Ancient Egyptian, classical Mayan, Chinese -- all probably related? This is not generally accepted.
It's an interesting idea, I cannot disprove it. But I don't think it has been proven, either. Even the possible relationship between Uralic, Afroasiatic and Indo-European is not widely accepted yet. Those language families are extensively documented and we can reconstruct their proto-languages convincingly back to somewhat around 10,000 years ago. They look kind of similar in some ways, maybe areal effects? I think to hope for another 10,000 years further back is too much. Borean is a claim about probably further back than even that. The Nostratic and Altaic subsets of the Borean hypothesis, presumably with its proto-language somewhere in Asia around 10,000 years ago, alone is controversial and is not generally accepted.
It's an interesting idea, I cannot disprove it. But I don't think it has been proven, either. Even the possible relationship between Uralic, Afroasiatic and Indo-European is not widely accepted yet. Those language families are extensively documented and we can reconstruct their proto-languages convincingly back to somewhat around 10,000 years ago. They look kind of similar in some ways, maybe areal effects? I think to hope for another 10,000 years further back is too much. Borean is a claim about probably further back than even that. The Nostratic and Altaic subsets of the Borean hypothesis, presumably with its proto-language somewhere in Asia around 10,000 years ago, alone is controversial and is not generally accepted.